An Ab Initio Approach to Closing the “10-100 eV Gap” for Charge-Carrier Thermalization in Semiconductors

We present here an ab initio study of the energy-loss processes and thermalization of hot carriers (electrons, holes, and/or electron-hole pairs) that are generated by high-energy radiation in wide-bandgap materials -- such as GaN, β-Ga₂O₃, C (in the diamond structure) and Si. In particular, we focus on the 10-100 eV range of kinetic energy (which we define as the “10-100 eV gap”), since this range is poorly understood. Indeed, the nuclear/particle physics community has a long-standing track record of understanding the thermalization in the higher-energy range (above about 100 eV), whereas the electronic-device community has studied extensively carrier transport in the lower-energy range (below ∼10 eV). However, the 10-100 eV gap has been studied only using the free-electron approximation and semi-empirical models for the energy-loss processes [1-3].
In order to close this 'gap', we have employed density functional theory (DFT) to obtain the band structure and the dielectric function of the materials, obtaining information about the electron dispersion and energy-loss function for energies up to about 100 eV. We have used DFT perturbation theory and Fermi’s Golden Rule/first Born approximation to calculate the charge-carrier scattering rates for the major charge-carrier interactions (phonon scattering, impact ionization, and plasmon emission). A full-band Monte Carlo solution of the Boltzmann transport equation is then used to study the thermalization of electrons with kinetic energies as high as 100 eV. Considering for example GaN, the results show that the full thermalization of electrons and holes is complete within ∼1 and 0.5 ps, respectively. Hot electrons dissipate about 90% of their initial kinetic energy to the electron-hole gas during the first ∼ 0.1 fs, due to rapid plasmon emission and impact ionization at high energies. The remaining energy is lost at a much slower rate via phonon emission at lower energies (below ∼10 eV). During the thermalization, hot electrons generate pairs with an average energy of ∼8.9 eV/pair (11-12 pairs per hot electron). Additionally, during the thermalization, the maximum electron displacement from its original position is found to be on the order of 100 nm [4].
Using the spatial and energetic distribution of the radiation-induced pairs, we have also performed full-band Monte Carlo simulations of electronic transport in devices. Considering a GaN/Al_0.32Ga_0.68N high electron mobility transistor (HEMT) as an example, we have calculated the damage induced by these hot electrons at the GaN/AlGaN interface using parameters (cross section and density of defect precursors) either determined experimentally or calculated using ab initio methods.
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